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If (\sqrt{n}) lies between (12) and (13), which value of (n) can be correct and makes (\sqrt{n}) irrational?
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Answer and explanation
Correct answer: (150)
Step 1: (12<\sqrt{n}<13) means (144<n<169). Step 2: (150) lies in this interval and is not a perfect square, so (\sqrt{150}) is irrational. Step 3: Square both bounds to handle square-root ranges.
Frequently asked questions
What is the correct answer to this question?
(150)
Why is this the correct answer?
Step 1: (12<\sqrt{n}<13) means (144<n<169). Step 2: (150) lies in this interval and is not a perfect square, so (\sqrt{150}) is irrational. Step 3: Square both bounds to handle square-root ranges.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Irrational numbers.
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